I would ask the PUArcade developer to let you know how best to do it. In other words, I'm not sure, but I would think saving your database and site to another directory prior to reinstalling Joomla would allow you to restore your previous tables from the backup directory to add the old data from your games after you repopulate the initial fields with the Joomla reinstall to give you your user data back.
I'm not an expert at restoring, so maybe someone has an easier way, but this way would at least keep your old tables/directories so no data is lost.
Anyone with more experience is welcome to jump on this one to confirm this is the best way or let us know a better way.
PS - I assume you don't have a bak_ file for the table you deleted or that would definitely be the easiest way to restore the table you lost.